There are a ton of sources for this info, and using the Search function on the site will help, as a bunch of guys post when they get drawn or fill their tag and how many points it took.
Not too complicated; but then again, i've been a resident for a few years now, and have it figured out. Need to do the same in other states now. There are a couple guys in this section that know way more about the process.
Buy a license, pick your hunt choices, Elk/Lope applications due by mid February, Deer/Sheep by early April. Non-residents get 10-15% of tag allocation per hunt. If you don't get drawn, you get a bonus point and your name goes in the pot 2x next year, and so on...
Elk/Lope Draw: Odds vary depending on unit, with the top units/hunts for non-residents taking 10-20 years. Other hunts can take much less. i.e. My dad (MO resident) got drawn for a late rifle bull hunt after 5 years. Tough hunt in a decent unit, but can be done.
Deer Draw: Same story as elk. If you're talking Strip or Kaibab, you're looking 10-20 years also. Other units, can take considerably less time.
"...I'd rather be tried by twelve than carried by six..."